code: def test_GPyTorchPosterior_Multitask(self):
      for dtype in (torch.float, torch.double):
          mean = torch.rand(3, 2, dtype=dtype, device=self.device)
          variance = 1 + torch.rand(
              3, 2, dtype=dtype, device=self.device
          )
          covar = variance.view(-1).diag()
          mvn = MultitaskMultivariateNormal(
              mean, to_linear_operator(covar)
          )
          posterior = GPyTorchPosterior(distribution=mvn)
          # basics
          self.assertEqual(posterior.device.type, self.device.type)
          self.assertTrue(posterior.dtype == dtype)
          self.assertEqual(
              posterior._extended_shape(), torch.Size([3, 2])
          )
          self.assertTrue(torch.equal(posterior.mean, mean))
          self.assertTrue(torch.equal(posterior.variance, variance))
          # rsample
          samples = posterior.rsample(sample_shape=torch.Size([4]))
          self.assertEqual(samples.shape, torch.Size([4, 3, 2]))
          samples2 = posterior.rsample(sample_shape=torch.Size([4, 2]))
          self.assertEqual(samples2.shape, torch.Size([4, 2, 3, 2]))
          # rsample w/ base samples
          base_samples = torch.randn(
              4, 3, 2, device=self.device, dtype=dtype
          )
          samples_b1 = posterior.rsample_from_base_samples(
              sample_shape=torch.Size([4]), base_samples=base_samples
          )
          samples_b2 = posterior.rsample_from_base_samples(
              sample_shape=torch.Size([4]), base_samples=base_samples
          )
          self.assertAllClose(samples_b1, samples_b2)
          base_samples2 = torch.randn(
              4, 2, 3, 2, device=self.device, dtype=dtype
          )
          samples2_b1 = posterior.rsample_from_base_samples(
              sample_shape=torch.Size([4, 2]),
              base_samples=base_samples2,
          )
          samples2_b2 = posterior.rsample_from_base_samples(
              sample_shape=torch.Size([4, 2]),
              base_samples=base_samples2,
          )
          self.assertAllClose(samples2_b1, samples2_b2)
          # collapse_batch_dims
          b_mean = torch.rand(2, 3, 2, dtype=dtype, device=self.device)
          b_variance = 1 + torch.rand(
              2, 3, 2, dtype=dtype, device=self.device
          )
          b_covar = torch.diag_embed(b_variance.view(2, 6))
          b_mvn = MultitaskMultivariateNormal(
              b_mean, to_linear_operator(b_covar)
          )
          b_posterior = GPyTorchPosterior(distribution=b_mvn)
          b_base_samples = torch.randn(
              4, 1, 3, 2, device=self.device, dtype=dtype
          )
          with self.assertWarnsRegex(
              DeprecationWarning, "`base_samples` with `rsample`"
          ):
              b_samples = b_posterior.rsample(
                  sample_shape=torch.Size([4]),
                  base_samples=b_base_samples,
              )
          self.assertEqual(b_samples.shape, torch.Size([4, 2, 3, 2]))
  
file_path: botorch/test/posteriors/test_gpytorch.py
imports: import itertools
  import warnings
  from contextlib import ExitStack
  from unittest import mock
  import torch
  from botorch.exceptions import BotorchTensorDimensionError
  from botorch.posteriors.gpytorch import GPyTorchPosterior, scalarize_posterior
  from botorch.utils.testing import _get_test_posterior, BotorchTestCase, MockPosterior
  from gpytorch import settings
  from gpytorch.distributions import MultitaskMultivariateNormal, MultivariateNormal
  from linear_operator.operators import to_linear_operator
  from torch.distributions.normal import Normal
label_desc: Use image node_id 2 for calling the TestGPyTorchPosterior obj's underlying member method code with example usage: obj.test_GPyTorchPosterior_Multitask() without return types